RE: composing functions

• To: mathgroup at smc.vnet.net
• Subject: [mg45545] RE: [mg45527] composing functions
• From: "David Park" <djmp at earthlink.net>
• Date: Tue, 13 Jan 2004 04:03:59 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Pedro,

If you take a off the list and put it in a Fold statement then you can use

list = {{f, g, h}, {b, c, d}};

Fold[First[#2][#1, Last[#2]] &, a, Transpose[list]]
h[g[f[a, b], c], d]

David Park

From: Pedro L [mailto:pedrito6 at softhome.net]
To: mathgroup at smc.vnet.net

Hi!

I  would  like  to find a way for composing a list of functions over a
list of numbers.

I  have  the  list  {{f,  g,  h},  {a,  b, c, d}}
(f, g, h are functions and a, b, c, d are numbers)
I would like to obtain h[g[f[a, b], c], d]

Since  it's  for a real program, I had to do it in "any" way. So I did
it as I show below:

In[1]:= kk = {{f, g, h}, {a, b, c, d}}

Out[1]= {{f, g, h}, {a, b, c, d}}

In[2]:= result1 = {kk[[2,1]]}; For[i = 1, i < Length[kk[[2]]], i++,
AppendTo[result1, kk[[1,i]]];
AppendTo[result1, kk[[2,i + 1]]]]; result1

Out[2]= {a, f, b, g, c, h, d}

In[3]:= result2 = StringJoin @@ ToString /@ result1

Out[3]= afbgchd

In[4]:= result3 = StringInsert[result2, "~", Range[2,
StringLength[result2]]]

Out[4]= a~f~b~g~c~h~d

In[5]:= result4 = ToExpression[result3]

Out[5]= h[g[f[a, b], c], d]

But I'm really sure that it can be done much better.

Could you help me?

```

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